8(3a+6)=a(2a-4)

Simple and best practice solution for 8(3a+6)=a(2a-4) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 8(3a+6)=a(2a-4) equation: 


Simplifying
8(3a + 6) = a(2a + -4)

Reorder the terms:
8(6 + 3a) = a(2a + -4)
(6 * 8 + 3a * 8) = a(2a + -4)
(48 + 24a) = a(2a + -4)

Reorder the terms:
48 + 24a = a(-4 + 2a)
48 + 24a = (-4 * a + 2a * a)
48 + 24a = (-4a + 2a2)

Solving
48 + 24a = -4a + 2a2

Solving for variable 'a'.

Combine like terms: 24a + 4a = 28a
48 + 28a + -2a2 = -4a + 2a2 + 4a + -2a2

Reorder the terms:
48 + 28a + -2a2 = -4a + 4a + 2a2 + -2a2

Combine like terms: -4a + 4a = 0
48 + 28a + -2a2 = 0 + 2a2 + -2a2
48 + 28a + -2a2 = 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
48 + 28a + -2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 14a + -1a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(24 + 14a + -1a2)' equal to zero and attempt to solve:

Simplifying
24 + 14a + -1a2 = 0

Solving
24 + 14a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-24 + -14a + a2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -14a + 24 + a2 = 0 + 24

Reorder the terms:
-24 + 24 + -14a + a2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -14a + a2 = 0 + 24
-14a + a2 = 0 + 24

Combine like terms: 0 + 24 = 24
-14a + a2 = 24

The a term is -14a.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14a + 49 + a2 = 24 + 49

Reorder the terms:
49 + -14a + a2 = 24 + 49

Combine like terms: 24 + 49 = 73
49 + -14a + a2 = 73

Factor a perfect square on the left side:
(a + -7)(a + -7) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(a + -7) equal to 8.544003745 and -8.544003745.


Subproblem 1
a + -7 = 8.544003745

Simplifying
a + -7 = 8.544003745

Reorder the terms:
-7 + a = 8.544003745

Solving
-7 + a = 8.544003745

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + a = 8.544003745 + 7

Combine like terms: -7 + 7 = 0
0 + a = 8.544003745 + 7
a = 8.544003745 + 7

Combine like terms: 8.544003745 + 7 = 15.544003745
a = 15.544003745

Simplifying
a = 15.544003745


Subproblem 2
a + -7 = -8.544003745

Simplifying
a + -7 = -8.544003745

Reorder the terms:
-7 + a = -8.544003745

Solving
-7 + a = -8.544003745

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + a = -8.544003745 + 7

Combine like terms: -7 + 7 = 0
0 + a = -8.544003745 + 7
a = -8.544003745 + 7

Combine like terms: -8.544003745 + 7 = -1.544003745
a = -1.544003745

Simplifying
a = -1.544003745


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {15.544003745, -1.544003745}
Solution
a = {15.544003745, -1.544003745}

See similar equations:

| 13n=36 | | B+(-2)=5 | | 6(2n+3)=10n | | 54y^4-9y^3= | | 9(a)=-54 | | -2n=12 | | 3(4b-10)=0.5(-24b+60) | | 3x+16=2x+14 | | 13y-8y=20 | | N-7=-11 | | 1.10=3+m | | 3x^2-9x-15=0 | | 2(4)+3(2.50)= | | -4y-3+3y+5=0 | | -8(3w-4)=16w | | 6-y=-5 | | 75+50(5)= | | 5(x+100)=2(x+100)+21 | | 2(m+7)+3m-3= | | 3z+3z=6 | | 56-m=30 | | 11-2(d-1)=-2+13 | | 6(y-3)-2y= | | 0.6-2.3=0.7 | | 5(n+2)-3= | | 8z+12z=9 | | 10-0.5=0 | | 4X+8Y=15 | | 5x+3x=23 | | p-(-4)=-6 | | 11j-3k-7-7j+3k= | | 7y+3(y-6)=5(y+2)-4 |

Equations solver categories